Daily Practice · Higher

January 2019 - Higher 5-a-day

Every Higher sheet published in January 2019, with answers. Grades 6-7 - Higher-tier method and manipulation.

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January 2019

31 sheets · 155 questions · Grades 6-7

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The batch download puts all 5 tiers' January 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in January 2019

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st January 2019A, B and C are points on a circle with centre O. Angle AOC is 122°. Work out angle ABC, where B is on the major arc.
  2. 2nd January 20194 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  3. 3rd January 2019A histogram class is 20 units wide and contains 60 values. Work out the frequency density.
  4. 4th January 2019Work out (64 x 10^11) / (8 x 10^3). Give your answer in standard form.
  5. 5th January 2019Expand and simplify (x + 4)(x - 3)(x - 4).
  6. 6th January 2019y is inversely proportional to x. When x = 6, y = 20. Work out y when x = 4.
  7. 7th January 2019A cone has base radius 3 cm and vertical height 24 cm. Work out its volume, leaving your answer in terms of pi.
  8. 8th January 201928 students study Spanish and 8 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  9. 9th January 2019Four classes in order have frequencies 10, 9, 6, 8. Write down the cumulative frequency at the end of the third class.
  10. 10th January 2019Write the recurring decimal 0.444... as a fraction in its simplest form.
  11. 11th January 2019Make x the subject of y = 2x^2 - 10.
  12. 12th January 2019y is directly proportional to x^2. When x = 4, y = 144. Work out y when x = 7.
  13. 13th January 2019In triangle ABC, angle A is 51°, angle B is 90° and side a is 19 cm. Use the sine rule to work out side b, to 1 decimal place.
  14. 14th January 20192 of 6 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  15. 15th January 201915 voles are marked and released. Later 96 are caught, of which 8 are marked. Estimate the population.
  16. 16th January 2019Work out 25^(3/2).
  17. 17th January 2019Factorise x^2 - 81.
  18. 18th January 2019y is directly proportional to x. When x = 3, y = 27. Work out y when x = 2.
  19. 19th January 2019A right-angled triangle has sides 8 cm, 15 cm and 17 cm. Work out the angle opposite the 8 cm side, to 1 decimal place.
  20. 20th January 201925 students study Spanish and 11 of those also study Art. One Spanish student is picked at random. Work out the probability they study Art.
  21. 21st January 2019A cumulative frequency graph is drawn for 84 values. What cumulative frequency do you read across from to estimate the lower quartile?
  22. 22nd January 2019Write sqrt(20) in the form a sqrt(b), where b is as small as possible.
  23. 23rd January 2019A region is defined by y < -x + 7. Should the boundary line be solid or dashed, and why?
  24. 24th January 2019A town's population is 31500 and grows by 4% each year. Work out the population after 4 years, to the nearest whole number.
  25. 25th January 2019The point (-1, 3) is enlarged by scale factor -1 about the centre (3, 3). Write down the coordinates of the image.
  26. 26th January 20191 of 5 bulbs in a box are faulty. Two are taken with replacement. Work out the probability at least one is faulty.
  27. 27th January 2019A box plot has a minimum of 4 and a maximum of 41. Work out the range.
  28. 28th January 2019A meal deal has 4 mains, 7 sides and 4 drinks. How many different meals are possible?
  29. 29th January 2019Factorise x^2 + 10x + 21.
  30. 30th January 2019A block has volume 160 cm^3 and density 8 g/cm^3. Work out its mass.
  31. 31st January 2019Two similar solids have lengths in the ratio 1 : 3. The larger has a volume of 351 cm^3. Work out the volume of the smaller.

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